 

Antun Milas and Michael Penn
Lattice vertex algebras and combinatorial bases: general case and Walgebras view print


Published: 
August 24, 2012 
Keywords: 
Vertex operator algebras, integral lattices 
Subject: 
17B69,17B67, 11P81 


Abstract
We introduce what we call the principal subalgebra of a lattice vertex (super) algebra
associated to an arbitrary Zbasis of the lattice.
In the first part (to appear), the second author considered the case of positive bases and found a description
of the principal subalgebra in terms of generators and relations. Here, in the most general case, we obtain a
combinatorial basis of the principal subalgebra W_{L} and of related modules.
In particular, we substantially generalize several results in Georgiev, 1996, covering the case of the root lattice of
type A_{n}, as well as some
results from Calinescu, Lepowsky and Milas, 2010.
We also discuss principal subalgebras inside certain extensions of affine Walgebras coming from multiples of the root lattice of type A_{n}.


Acknowledgements
The first author graciously acknowledges support from NSA and NSF grants.


Author information
Antun Milas:
Max Planck Institute für Mathematik, Vivatsgasse 7, Bonn, Germany
Department of Mathematics and Statistics, University
at Albany (SUNY), Albany, NY 12222
amilas@math.albany.edu
Michael Penn:
Department of Mathematics, University of Tennessee, Chattanooga
michaelpenn@utc.edu

